| Issue |
EPL
Volume 85, Number 2, January 2009
|
|
|---|---|---|
| Article Number | 20008 | |
| Number of page(s) | 6 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/85/20008 | |
| Published online | 30 January 2009 | |
Log-periodic modulation in one-dimensional random walks
Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR) and Departamento de Física FCEyN, Universidad Nacional de Mar del Plata - Deán Funes 3350, (7600) Mar del Plata, Argentina
Corresponding author: iguain@mdp.edu.ar
Received:
9
October
2008
Accepted:
22
December
2008
We have studied the diffusion of a single particle on a one-dimensional lattice. It is shown that, for a self-similar distribution of hopping rates, the time dependence of the mean-square displacement follows an anomalous power law modulated by logarithmic periodic oscillations. The origin of this modulation is due to the dependence of the diffusion coefficient on the length scale. Both the random walk exponent and the period of the modulation are analytically calculated and confirmed by Monte Carlo simulations.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.40.Fb – Random walks and Levy flights / 66.30.-h – Diffusion in solids
© EPLA, 2009
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